This proposal is to provide travel support to US participants to the conference Derived Categories of Algebro-Geometric Origin and Integrable Systems to be held in Jerusalem, Israel, December 19-24, 2010. The conference is organized by the PI together with Dennis Gaitsgory (Harvard) and David Kazhdan (Hebrew University). The purpose of this conference is to bring together leading experts in related directions at the borderline of representation theory, algebraic geometry, and quantum field theory, with the goal of uncovering the nature of observed connections and promoting progress in each of the subjects. This conference will cover the following topics: 1) Wall-crossing phenomenon in algebraic geometry and representation theory; generalizations of Kazhdan-Lusztig theory and their relation to Bridgeland stability and quantum cohomology. 2) Categorical dualities and their relation to quantum field theory: geometric Langlands duality, homological mirror symmetry. Higher categorical structures arising in algebraic geometry, representation theory and quantum field theory. 3) New questions of representation theory coming from gauge theory and Liouville theory. These topics cover recent new development of representation theory and algebraic geometric approach to questions in geometry and mathematical physics.
Interactions of different mathematical science research fields and other science areas always stimulate new discoveries. This research conference is to interact researchers in several different areas of mathematical and physical sciences. Recent new discoveries in the fields have further strengthened such interactions. Several young US scientists will participate this conference and it will help them to establish themselves in these fields to be the future leaders in the fields.
" held on December 19-24, 2010 at the Institute for Advanced Studies of Hebrew University in Jerusalem, Israel. The conference was the culmination of a semester long special program held at the Institute, though it also explored topics beyond those covered during the semester. Leading experts from the US, France and Japan were among the speakers,while the audience included a number of graduate students and postdocs, many of them from the US, as well as senior mathematicians working on related subjects. Ideas coming from physics have been a major impetus for developement of mathematics throughout its history. The conference was devoted to new connections of some fundamental concepts of mathematical physics, such as integrable systems related to quantum field theory to questions traditionally studied in algebra and algebraic geometry. The particular mathematical questions the conference was focused on are about numerics of representations (where by a representation one understands a linear algebraic structure related to symmetries) and categorical invariants of geometric objects studied in algebraic geometry . Such connections are known or expected to provide essentially new methods for the mathematical theories involved. Altogether, the conference was a major contribution to dissemination of knowledge and exchange of ideas in an active research area.
